Recent content by Sleepycoaster

Okay, thanks!

Homework Statement Show that the energy of an ideal dipole p in an electric field E is given by U = -p ⋅ E Homework Equations Work = θτ where τ is torque τ = p × E The Attempt at a Solution U = ∫(p × E) dθ' (from θ to 0, since the dipole will eventually align itself with the magnetic...

Thanks for replying. This is a problem from a book on Electricity and Magnetism that my university is using. I don't really understand the partial derivative over n-hat myself, and the book doesn't mention it in detail. I'll drop this topic and ask my professor if he knows.

Homework Statement Prove Eqn. 1 (below) using Eqns. 2-4. [Suggestion: I'd set up Cartesian coordinates at the surface, with z perpendicular to the surface and x parallel to the current.] Homework Equations I used ϑ for partial derivatives. Eqn. 1: ϑAabove/ϑn - ϑAbelow/ϑn = -μ0K Eqn. 2: ∇ ⋅ A...

I'm afraid I don't know space-time diagrams very well. Do you mean, a graph with perpendicular axes "time" and "distance" with a second "time" axis at slope 1/.7 and a second "distance" axis at slope .7, all from the origin?

Okay, I figured it out. From my point of view, the bird flew north at .82645c, but if I were to use a simple Lorentz contraction and multiply this velocity by sqrt(1-(.7)^2), you get a velocity of .5902c north, which, coupled with the .23608c component East, will get the bird to the birdfeeder.

Dauto, Thanks for the reply, but I'm not sure I get it. Wouldn't the Einstein velocity transformations already account for the space contraction between the points of view of me and the frisbee?

So I made this problem up to visualize the einstein velocity transformations between inertial frames. Homework Statement I throw a frisbee due north. It goes north at a constant velocity of .7c. At the same time I throw it, a bird flies in a straight line at a constant velocity of .5c at such...

My question is simple: Why do batteries need electrolytes? Wouldn't the battery need the charge to flow only through the circuit in the device being powered? The point of the anode and cathode's separation is to preserve the potential difference, so why allow charge to flow through an electrolyte?

Thank you, I'll definitely consider that detail.

Homework Statement Imagine two synchronized atomic clocks with hands that turn at the same rate. Put one of these on a plane starting in NYC and fly it around the world once, and leave the other at NYC. Because the one that flew supposedly took a more convoluted path, it should be behind the...

Homework Statement There's no specific question, but mostly a theory I wanted clarified. According to my textbook, the measurement of the total mechanical energy E of a mass orbiting a much larger mass in an ellipse is: E = radial (change in radius) kinetic energy + rotational kinetic energy...

Oh hey, I see where I went wrong. I took the derivative when I should have taken the integral. Thank you!

And yes, everything in this proof refers to a sphere with radius 1.

Homework Statement I know how to find the volume of a sphere just by adding the areas of circles, so I decided to do a double integral to find the same volume, just for fun. Here's what I've set up. I put 8 out front and designed the integrals to find an eighth of a sphere that has its center...